6 Mar 2017: Lab 6: Propagated Uncertainty in Measurements

Lab 6:

Propagated Uncertainty in Measurements

Joel Cook

Nina Song

Lab performed March 6, 2017

Introduction: In this lab we are practicing calculating the propagation of uncertainty in measurements by calculating the density of two cylinders and the uncertainty in the values.

Procedure: Calipers were used to measure the height and diameter of two cylinders. A digital scale was used to measure the mass of the cylinders. The height, diameter, and mass are used to then calculate the density. 

Data and Calculations:

	Mass (g)	Height (cm)	Diameter (cm)
Cylinder 1	69.4	3.42	1.88
Cylinder 2	27.6	5.03	1.58

ρ=    m   =      m    

           V       π (D/2)²h

Density of cylinder 1:

ρ=   69.4

         π(1.88/2)² *3.42

=7.30g/cm^3

Density of cylinder 2:

ρ=   27.6 

         π(1.58/2)² *5.03

=2.80g/cm^3

Calculating propagated uncertainty:

Density of cylinder 1 is 7.30 +/- 0.08 g/cm^3 (Accepted density of zinc is 7.13 g/cm^3)

Density of cylinder 2 is 2.80 +/- 0.04 g/cm^3 (Accepted density of aluminum is 2.70 g/cm^3)

Conclusion: The density we calculated for each cylinder was acceptably close to the accepted densities of each material, based on the conditions of the experiment. Uncertainty exists in the experiment in both the measurements taken, through accuracy of tools used, and in the purity of the samples used. Based on these uncertainties, the results of the lab are acceptable.